Heat Transfer Analysis of MHD Flow in a Porous Tube Under Local Thermal Nonequilibrium Conditions Using the Keller-Box Method

The present study investigates heat transfer characteristics in the thermally developing region of a porous tube under the local thermal nonequilibrium (LTNE) model. The influence of magnetohydrodynamic (MHD) flow on an electrically conducting fluid flowing through a porous medium under a transverse magnetic field is examined. Under the LTNE framework, two separate energy equations are employed to describe the temperature fields of the fluid and solid phases. The coupled governing equations are solved numerically using the Keller-box method. The results indicate that increasing the interphase heat transfer parameter strengthens thermal coupling between the fluid and solid phases, thereby reducing temperature differences and promoting local thermal equilibrium. In contrast, an increase in the Prandtl number reduces thermal diffusion, leading to larger temperature gradients and greater disparity between the two phases. Furthermore, the magnetic field suppresses both the velocity and temperature distributions through the Lorentz force. An increase in permeability reduces the velocity profiles due to the combined effects of the MHD and Prandtl numbers while increasing the temperature profiles. Increasing the interphase heat transfer rate drives the system from the LTNE to the LTE phase. The study confirms that LTNE effects play a significant role in thermal transfer processes in porous media and are relevant for various industrial heat transfer applications.